opposite of bwmorph thicken

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Hi All,
'thicken' in bwmorph adds pixels to the exterior of objects without changing the EULER number. Is there a way to do the opposite....i.e. take away pixels from the exterior of objects without changing the Euler number? 'erode' does not fulfil this requirement.

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Image Analyst
Image Analyst 2014-1-3
Use the skel option of bwmorph: " With n = Inf, removes pixels on the boundaries of objects but does not allow objects to break apart. The pixels remaining make up the image skeleton. This option preserves the Euler number. " You can use n less than inf if you want.

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